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    <title>杠杆原理实验 - 说明</title>
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<body>
    <div class="container">
        <div class="intro-section">
            <h1>杠杆原理实验</h1>
            <p>探索力矩平衡和机械优势，理解简单机械的工作原理</p>
        </div>
        
        <div class="md3-card card-primary">
            <div class="card-header">实验原理</div>
            <div class="card-body">
                <p>杠杆是最基本的简单机械之一，它由一个支点和一个刚性杆组成。杠杆的工作原理基于力矩平衡，当杠杆处于平衡状态时，支点两侧的力矩大小相等但方向相反。</p>
                <div class="formula">
                    <div class="katex-formula">
                        \[ \tau = F \times r \times \sin(\theta) \]
                    </div>
                    <p>其中：</p>
                    <div class="katex-formula">
                        \[ \begin{array}{rcl}
                        F & = & \text{作用力的大小} \\
                        r & = & \text{力臂（从支点到力的作用线的垂直距离）} \\
                        \theta & = & \text{力的方向与杠杆的夹角}
                        \end{array} \]
                    </div>
                </div>
            </div>
        </div>
        
        <div class="card md3-card card-secondary">
            <div class="card-header">
                <h2>数学表达</h2>
            </div>
            <div class="card-body">
                <p>杠杆平衡的基本条件（力矩平衡）：</p>
                <div class="katex-formula">
                    \[ F_1d_1 = F_2d_2 \]
                </div>
                <p>其中\(F_1\)、\(F_2\)为作用力，\(d_1\)、\(d_2\)为力臂。</p>
                <p>机械效率：</p>
                <div class="katex-formula">
                    \[ \eta = \frac{W_{\text{输出}}}{W_{\text{输入}}} \times 100\% \]
                </div>
                <p>力的关系：</p>
                <div class="katex-formula">
                    \[ \frac{F_1}{F_2} = \frac{d_2}{d_1} \]
                </div>
                <p>功的关系：</p>
                <div class="katex-formula">
                    \[ F_1s_1 = F_2s_2 \]
                </div>
                <p>其中s<sub>1</sub>、s<sub>2</sub>为位移。</p>
            </div>
        </div>
        
        <div class="md3-card card-tertiary">
            <div class="card-header">实验要点</div>
            <div class="card-body">
                <ul class="key-points">
                    <li>理解力矩的概念和计算方法</li>
                    <li>验证杠杆平衡条件</li>
                    <li>探索力臂长度对机械优势的影响</li>
                    <li>分析力的方向对力矩的影响</li>
                    <li>掌握杠杆的应用原理</li>
                </ul>
            </div>
        </div>
        
        <div class="md3-card card-surface">
            <div class="card-header">实验目标</div>
            <div class="card-body">
                <p>1. 理解力矩的概念和计算方法</p>
                <p>2. 验证杠杆平衡条件</p>
                <p>3. 探索力臂长度、作用力大小和方向对力矩的影响</p>
                <p>4. 计算和验证不同情况下的机械优势</p>
            </div>
        </div>
        
        <div class="text-center mt-4">
            <a href="/lever" class="md3-btn md3-btn-primary">开始实验</a>
            <a href="/" class="md3-btn md3-btn-secondary">返回首页</a>
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